This is little weird. I get access token by clicking on Get Access Token and then selecting offline_access, manage_permissions, publish_stream. But when I again try to Get Access Token, All other permissions except offline_access are checked while my previous access token should have made it checked.
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RandomQuestionApr 6 '12 at 23:42

What kind of Access Token do you need? There are three kinds, User AT, App AT and Page AT.

If you want User AT, it seems you are out of luck. I don't think it's possible anymore. You can only get to 60 days. However, if you need Page AT, you can get a permanent one. The difference is, Page Access Token only has access to a single facebook page.

Basically you need to get User Access Token first, with manage_pages permission. When you have one, you have to look at /{pageId}?fields=access_token for your page's id in Graph API.

you will not get any permanent access token as Facebook developer blog explains. you will be given 60 days long lived access token. Before the expiration Facebook will notify you about the expiry and then you can renew it or you can build your own custom control to get the notification on token expiration which you can fetch from Facebook API.